Proposition 1:The Nature of the Lifetime-Profitability Relationship is Positive
Lifetime-Profitability Association Segmentation Scheme
Lifetime Profit Low High Lifetime revenue High Low Short Long Lifetime duration Segment 2 Segment 3 Segment 4 Segment 1 Long Lifetime Duration Short
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Customer Lifetime and Firm Profitability : Proposition 2: Profits Increase over Time
Analysis of the dynamic aspects of the lifetime-profitability relationship
Non-contractual setting: cost of serving customer can easily exceed the profit margin brought in by the customer. Therefore, profits may not increase over time
Example: catalog shopping or direct mail offerings - the customer may end up buying once a year and spend a smaller amount
Existing customers pay effectively higher prices than new ones, even after accounting for possible introductory offers
OR
Higher value consciousness of long-term customers because customers learn over time to trust lower priced items or brands rather than established name brand products
Model for Measuring Customer Lifetime for Non-Contractual Relationships
Negative Binomial Distribution (NBD)/Pareto model
Based on the customer-specific probability of being alive, the model can be used to determine which customers should be deleted from active status
Given that the outcome of the NBD/Pareto model is a continuous probability estimate, continuous P(Alive) estimate is transformed into a dichotomous “alive/dead” measure
Knowing a person’s “time of birth” and given a specified probability level threshold), can approximate when a customer is deemed to have left the relationship
The time from birth, t 0 , until the date associated with the cut-off threshold, t cut-off , constitutes the lifetime of the customer
Calculate finite lifetime for each customer, for profitability analysis
Research Methodology
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Illustrative Lifetime Determination of Individual Household Source: Reinartz W. And Kumar V., “On the Profitability of Long –life Customers in a Non-Contractual Setting: An empirical Investigation and Implications for Marketing
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Measuring Customer Lifetime for Non-Contractual Relationships (contd.)
Establishment of Cut-off Threshold
E stablishment of cut-off threshold that produces the highest percentage of correct classifications (here 0.5)
Lifetime Estimation
Finite Lifetime Estimates
35 12 41.7 7.9 27.9 Cohort 2 36 11 41.1 7.8 28.7 Cohort 1 Maximum Minimum % Right- Censored Standard deviation Mean Lifetime (months)
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Measuring Customer Lifetime for Non-Contractual Relationships (contd.)
Profit Calculation
Net-present value of profit is calculated on an individual customer basis for the period of 36 months as:
where LT i = individual net-present lifetime profit for 36 months
GCti = gross contribution in month t for customer i ,
Cti = mailing cost in month t for customer i ,
0.0125 = monthly discount rate (based on 0.15 rate per year)
Could customers with shorter tenure might actually be more profitable than long-term customers, a claim that runs counter to the theoretical expectations of a relationship perspective?
Which group of customers is of more interest to the firm, the one that buys heavily for a short period or the one with small spending but with long-term commitment?
The mean relative profit for each segment is significantly different from the other segment at least at = 0.05 (using the multiple comparison test)
Segment 1 customers are the most desirable set for the firm –
represents the loyalty effect at its best
For Segment 3 customers (high revenue but short lifetime), there appears to be a good match between offerings and desires but their relationship duration may be complicated by moderating factors
Dissatisfaction might occur for Segment 4 whose customers spend the lowest amount
Regression Results for t = 1 to 36 Months (Cohort 1) Validation Results in Parentheses (Cohort 2)
With the exception of Segment 2, the coefficient for the linear effect has a negative sign – highlights the negative profit trend over time for the 3 segments
All the coefficients for time are significant at =0.01
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Are the Costs of Serving Long-Life Customers Lower?
The ratio of mailing cost per dollar sales in the longer-life segment (Segment 1) is statistically not different from the mailing cost per dollar sales in the shorter-life segment (Segment 3)
In terms of cost efficiency, Segments 1 and 3 are the most attractive to the firm, although they have very different lifetime properties
The ratio of mailing cost and revenues – which is one measure of efficiency – need not necessarily be lower for long-life-customers
A strong linear positive association between lifetime and profits does not necessarily exist
A static and a dynamic lifetime-profit analysis can exhibit a much differentiated picture: profitability can occur for the firm from high and low lifetime customers
Profits do not increase with increasing customer tenure: the cost of serving long-life customers is not lower
Long-life customers do not pay higher prices
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Study 2: A model for Incorporating Customers’ Projected Profitability into Lifetime Duration Computation
Determine the contribution margin expected from each customer
in future periods based on the average of the contribution margins in the past
Determine for each future period, the probability that the customer will be alive and will transact with the firm
Combine these two components
Discount the expected contribution margin in each future period to its
Net Present Value (NPV) using the cost of capital applicable to the firm
If in a given month, cost of additional marketing efforts is greater than NPV, determine that the Profitable Lifetime Duration of the customer has ended
Predictor variables to incorporate into the model:
Exchange variables: e.g. Amount Purchased, Degree of Cross-buying, Degree of Focused-buying, Inter-purchase Time, Number of Product Returns, Ownership of Loyalty Instruments, and Mailing efforts undertaken by the firm
Customer Heterogeneity variables: e.g. Location and Income of the customer
Conceptually,
Profitable Lifetime = f (Exchange characteristics, Customer heterogeneity)
Calculation of net present value (NPV) of expected contribution margin (ECM it ):
NPV of ECM it = where ECM it = estimated expected contribution margin for a given month t , AMCM it = average contribution margin in month t based on all prior purchases since birth (updated dynamically), r = discount rate (15% on a yearly basis) i = the customer t = month for which NPV is estimated n = number of months beyond t , P( Alive) in = probability that customer i is alive in month n .
In the proportional hazard model, the hazard rate hi(t) for individual i is assumed to take the form:
where
h 0 (t) is the baseline hazard rate
(x it ) is the impact of the independent variables
h i (t) = h 0 (t) e x it
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Variables for Profitable Lifetime Model (-)Inverse U-shaped relationship for AIT and AIT 2 (Number of Days) 2 (Average Interpurchase Time it ) 2 (+) Inverse U-shaped relationship for AIT and AIT 2 Number of Days Average Interpurchase Time it Non-directional hypothesis Dummy: 1 = buys consistently in single dept. only 0 = all other Focus of Buying i (+) Number of departments shopped in Cross Buying it + Monthly spending level ($), moving average over 6 month period Purchase amount it ** Hypothesized Directional Impact on Profitable Lifetime Measured as Independent Variables Months Profitable Lifetime i * Measured as Dependent Variable
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Variables for Profitable Lifetime Model (contd.) No directional hypothesis Age of individual in years Age i (+) Scale from 1 to 9 where 1 is < $10,000 and 9 is > 150,000 Income i (-) Number of people in 2 digit zip code Population Density No directional hypothesis 1 = more than 50 % of purchases in softgoods, 0 = more than 50 % of purchases in hardgoods Product Category i (+) Number of mailings sent in last 6 months (= 1 season) since current t , exponential decay, one month lag Mailings it (+) Ownership of Charge card. Dummy variable, 1 = owns card, 0 = no card Loyalty Instrument i (-) Proportion of returns (of sales) Returns it
The hazard of a lifetime event of a household i at time t is given as:
h i (t) = h 0 (t) EXP (β 1 Purchase Amount it + β 2 Cross Buying it + β 3 Focus of Buying i + β 4 Average Interpurchase Time it + β 5 (Average Interpurchase Time it ) 2 + γ 1 Returns it + γ 2 Loyalty Instrument i + γ 3 Mailings it + γ 4 Product Category i + δ 1 Population Density i + δ 2 Income i + δ 3 Age i )
36.
Summary of Results Supported However, the relationship is negative, indicating that buying in only a single department results in shorter lifetime duration Supported However, the relationship is negative, indicating that buying in only a single department results in shorter lifetime duration Related to the Focused Buying behavior exhibited by customers 2 b Partial Support Only the linear term is significant Supported Related to Average Interpurchase Time in an inverse U-shaped manner whereby intermediate AIT is associated with the longest profitable lifetime 3 Not Supported However, the interaction of Returns with Purchase amount variable is significant Not Supported However, the interaction of Returns with Purchase amount variable is significant Inversely related to the proportion of merchandise returned by the customers. 4 Supported Supported Positively related to degree of cross-buying behavior exhibited by customers 2 a Supported Supported Positively related to the customer’s spending level 1 B-to-B Setting Result B-to-C Setting Result Description Profitable Customer Lifetime Duration is: Hypothesis
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Summary of Results (contd.) Supported Supported Profitable Customer Lifetime Duration is positively related to the Income of the customer (B-to-C) or Income of the firm (B-to-B) 8 Not supported Supported Profitable Customer Lifetime Duration is higher for customers living in areas with lower population density (B-to-C) or businesses existing in lower population density (B-to-B) 7 Supported Supported Positively related to the number of mailing efforts of the company (B-to-C) or the number of contacts (B-to-B) 6 Supported Supported Positively related to the customer’s ownership of the company’s loyalty instrument (B-to-C) or the availability of line of credit (B-to-B) 5
Probability that a customer with a particular observed transaction history is still alive at time T since trial:
P [Alive | r, , s, , x, t, T] =
where a 1 = r+x+s, b 1 = s+1, c 1 = r+x+s+1, z 1 (y) = ( - ) / ( +y),
F(a 1 , b 1 ; c 1 ; z 1 ) is the Gauss hyper geometric function,
r, , s, = model parameters,
x = number of purchases,
t = time since trial at which the most recent transaction occurred,
T = time since trial
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Study 3 – A Model for Identifying the True Value of a Lost Customer
Conceptual Background
The value of a lost customer depends upon whether:
the customer defects to a competing firm or
disadopts the product category
Defection: The firm loses direct sales that customer would have brought in
Disadoption: Customer stops purchasing from that product category altogether
Affects the long term profitability by :
The loss of direct sales
Indirect effects of word of mouth, imitation, and other social effects
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Modeling the Effects of Disadoption on the Value of a Lost Customer
Value of an average lost customer (VLC) is calculated as:
VLC = VLC disadopter + (1- ) VLC defectors
where is the proportion of disadopters in a firm’s lost customers
Profit impact of a lost customer = sales estimate from new product growth model without disadoption – the sales estimate when the customer disadopts after certain time
42.
Modeling the Effects of Disadoption on the Value of a Lost Customer (contd.)
Key determinants of the value of a lost customer:
The time when customer disadopts has the largest impact on the value of the lost customer; earlier disadoption causes more loss of money
The external influence, p has a negative impact
The internal influence, q has a positive impact on penetration because higher q signifies stronger word of mouth
Discount rate has positive impact on the value of lost customer
A study of the Life-time-Profitability relationship in a non-contractual setting highlights concern with the widespread assumption of a clear-cut positive lifetime-profitability relationship and underlines the importance of a differentiated analysis
The empirical evidence showed that (1) a strong linear positive association between lifetime and profits does not necessarily exist; (2) profits do not necessarily increase with increasing customer tenure, (3) the cost of serving long-life customers is not lower, and (4) long-life customers do not pay higher prices
The main drivers of customer’s profitable lifetime duration are classified as exchange characteristics and customer heterogeneity
The key determinants of the value of a lost customer are identified as disadoption time, external and internal influences and the discount rate
The disadoption time is found to have the maximum negative impact on the value
i.e., the earlier a customer disadopts, the higher is the value of the lost customer
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